Решебник самостоятельные и по алгебре 7 класс Глазков контрольные работы КР-10. Итоговая Вариант 3

\[\boxed{Вариант\ 3.}\]

\[\boxed{\mathbf{1.}}\]

\[y = 6x - 12\]

\[y = 18:\]

\[6x - 12 = 18\]

\[6x = 18 + 12\]

\[6x = 30\]

\[x = 5.\]

\[Ответ:1)\ 5.\]

\[\boxed{\mathbf{2.}}\]

\[\frac{8^{2} \cdot 8^{9}}{\left( 8^{2} \right)^{4}} - 18^{2} + 28^{0} = \frac{8^{11}}{8^{8}} - 324 + 1 =\]

\[= 8^{3} - 323 = 512 - 323 = 189.\]

\[Ответ:4)\ 189.\]

\[\boxed{\mathbf{3.}}\]

\[\left\{ \begin{matrix} 8 \cdot (4x - 3) - 9 \cdot (2y - 3) = 13 \\ 0,7x + 0,3y = 2,3\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ | \cdot 10 \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 32x - 24 - 18y + 27 = 13 \\ 7x + 3y = 23\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 32x - 18y = 10\ \ \ \ \ \ \ \\ 7x + 3y = 23\ \ | \cdot 6\ \ \ \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} 32x - 18y = 10\ \ \ \\ 42x + 18y = 138 \\ \end{matrix} \right.\ ( + )\]

\[74x = 148\]

\[x = 148\ :74\]

\[x = 2.\]

\[3y = 23 - 7x = 23 - 7 \cdot 2 = 23 - 14\]

\[3y = 9\]

\[y = 3.\]

\[\left\{ \begin{matrix} x_{0} = 2 \\ y_{0} = 3 \\ \end{matrix} \right.\ \]

\[x_{0} - y_{0} = 2 - 3 = - 1.\]

\[Ответ:3) - 1.\]

\[\boxed{\mathbf{4.}}\]

\[Упорядочим\ ряд\ данных:\]

\[12;12;12;17;17;20.\]

\[Мода:12.\]

\[Медиана:(12 + 17)\ :2 = 14,5.\]

\[Среднее\ арифметическое:\]

\[\frac{12 \cdot 3 + 17 \cdot 2 + 20}{6} = \frac{36 + 34 + 20}{6} =\]

\[= \frac{90}{6} = 15.\]

\[Ответ:12;\ \ 14,5;\ \ 15.\]

\[\boxed{\mathbf{5.}}\]

\[x^{3} + 27y^{3} - 3x^{2}y - 9xy^{2} =\]

\[= (x + 3y)\left( x^{2} - 3xy + 9y^{2} \right) - 3xy(x + 3y) =\]

\[= (x + 3y)\left( x^{2} - 3xy + 9y^{2} - 3xy \right) =\]

\[(x + 3y)\left( x^{2} - 6xy + 9y^{2} \right) =\]

\[= (x + 3y)(x - 3y)^{2}\]

\[\boxed{\mathbf{6.}}\]

\[Пусть\ \text{x\ }лет - бабушке;y\ лет - внуку.\]

\[Составим\ систему\ уравнений:\]

\[\left\{ \begin{matrix} x = 3y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x - 20 = 11 \cdot (y - 20) \\ \end{matrix} \right.\ \]

\[\left\{ \begin{matrix} x = 3y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = 11y - 220 + 20 \\ \end{matrix} \right.\ \Longrightarrow \left\{ \begin{matrix} x = 3y\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ x = 11y - 200 \\ \end{matrix} \right.\ \]

\[11y - 200 = 3y\]

\[11y - 3y = 200\]

\[8y = 200\]

\[y = 200\ :8 = 25\ (лет) - внуку.\]

\[25 \cdot 3 = 75\ (лет) - бабушке.\]

\[Ответ:75\ лет.\]